W06D1 Current, Current Density, Resistance and Ohm’s Law, Magnetic Field, Magnetic Force
Today’s Reading Assignment: Current, Current Density, and Resistance and Ohm’s Law, Magnetic Fields and Forces Course Notes:
Sections 6.1-6.5, 8.1-8.3 1 Announcements
Week 6 Problem Solving and Math Review Tuesday from 9-11 pm in 26-152
PS 5 due Week 6 Tuesday at 9 pm in boxes outside 32-082 or 26-152
W06D2 Reading Assignment Course Notes: Magnetic Forces, Currents & Dipoles; Sections 8.3, 9.1-9.2
Exam 2 Thursday March 21 7:30 - 9:30 pm
2 Outline
Current and Current Density
Resistance and Ohm’s Law
Magnetic Field
Magnetic Forces
3 Current: Flow Of Charge
Average current Iav: Charge flowing across area A in time
Instantaneous current: differential limit of Iav
Units of Current: Coulomb/second = Ampere
4 How Big is an Ampere? • Household Electronics ~1 A • Battery Powered ~100 mA (1-10 A-Hr) • Household Service 100 A • Lightning Bolt 10 to 100 kA
• To hurt you 40 (5) mA DC(AC) • To throw you 60 (15) mA DC(AC) • To kill you 0.5 (0.1) A DC(AC)
• Fuse/Circuit Breaker 15-30 A
5 Direction of the Current Direction of current is direction of flow of pos. charge
or, opposite direction of flow of negative charge
6 Why Does Current Flow?
If an electric field is set up in a conductor, charge will move (making a current in direction of E)
Note that when current is flowing, the conductor is not an equipotential surface (and Einside ≠ 0)!
7 Microscopic Picture
Drift velocity is the average velocity forced by applied electric field in the presence of collisions. Magnitude is typically 4x10-5 m/sec, or 0.04 mm/ second! To go one meter at this speed takes about 10 hours! 8 Summary
Current:
Charge
Displacement
Drift speed
9 Current Density J Let n = number of charged objects per unit volume q = charge of object = drift velocity of object The current density is current per unit area
Generalization for many charged moving objects
10 Current and Current Density J
Current is the flow (flux) of current density through an open surface
Special case: uniform and perpendicular to surface
11 Concept Question: Current Density A current I = 200 mA flows in the wire below. What is the magnitude of the current density J?
5 cm 10 cm 1. J = 40 mA/cm 20 cm 2. J = 20 mA/cm 3. J = 10 mA/cm 4. J = 1 mA/cm2 5. J = 2 mA/cm2 6. J = 4 mA/cm2
P18- 12 Conductivity and Resistivity Ability of current to flow depends on density of charges & rate of scattering
Two quantities summarize this:
σc: conductivity
ρr: resistivity
13 Microscopic Ohm’s Law
and depend only on the microscopic properties of the material, not on its shape
14 Demonstrations:
Temperature Effects on Resistance F4
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F%204&show=0 Conducting Glass F1
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F%201&show=0 Conductivity of Ionizing Water F5
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F%205&show=0
15 Why Does Current Flow? Instead of thinking of Electric Field, think of potential difference across the conductor
16 Ohm’s Law What is relationship between electric potential difference and current?
17 Ohm’s Law
R has units of Ohms (W) = Volts/Amp 18 How Big is an Ohm? • Short Copper Wire milliohms (m ) • Notebook paper (thru) ~1 G • Typical resistors to 100 M
• You (when dry) 100 k • You (when wet) 1 k • Internally (hand to foot) 500
Stick your wet fingers in an electrical socket: You’re dead! 19 Concept Question: Resistance When a current flows in a wire of length L and cross sectional area A, the resistance of the wire is
1. Proportional to A; inversely proportional to L. 2. Proportional to both A and L. 3. Proportional to L; inversely proportional to A. 4. Inversely proportional to both L and A
P18- 20 Group Problem: Calculating Resistance Consider a material of resistivity in a shape of a truncated cone of altitude h, and radii a and b, for the right and the left ends, respectively, as shown in the figure. Assuming that the current is distributed uniformly throughout the cross-section of the cone, what is the resistance between the two du 1 ends? You may find the = − ∫ 2 following integral useful (where (αu + β) α(αu + β) and are constants).
21 Magnetic Fields
22 Magnetic Field of the Earth
North magnetic pole located in southern hemisphere
http://www.youtube.com/watch?v=AtDAOxaJ4Ms 23 Demonstrations:
Magnetic Field Lines of a Bar Magnet G2 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%202&show=0
Magnetic Field Lines of a Single Wire G12
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2012&show=0
24 How Big is a Tesla? • Earth’s Field 5 x 10-5 T = 0.5 Gauss • Brain (at scalp) ~1 fT • Refrigerator Magnet 1 mT • Inside MRI 3 T • Good NMR Magnet 18 T • Biggest in Lab 150 T (pulsed) • Biggest in Pulsars 108 T
25 Moving Charges Feel Magnetic Force
Magnetic force perpendicular both to: Velocity v of charge and magnetic field B 26 Concept Question: Units Magnetic Field What are the correct SI units for the magnetic field?
1. C/N-m-s 2. N-m-s/C 3. N/C 4. N-s/C-m 5. C-m/N-s
P18- 27 Cross Product: Magnitude
Computing magnitude of cross product A x B:
area of parallelogram 28 Cross Product: Direction
Right Hand Rule #1:
For this method, keep your hand flat! 1) Put Thumb (of right hand) along A 2) Rotate hand so fingers point along B 3) Palm will point along C
29 Cross Product: Signs
Cross Product is Cyclic (left column) Anti-commutative:
Switching vectors changes sign (right column)30 Concept Question: Cross Product
An electron is traveling to the right with speed v in a magnetic field that points up. What is the direction of the force on the electron 1. up 2. down 3. left 4. right 5. into page 6. out of page
P18- 31 Demonstration: Magnetic Deflection of TV Image G6
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%206&show=0
32 Concept Question: Force Direction Is this picture (deflection direction) correct?
1. Yes 2. No 3. I don’t know 33 Putting it Together: Lorentz Force
Force on charged particles in electric and magnetic fields
Electric Force Magnetic Force
34 Velocity Selector
Particle moves in a straight line when
35 What Kind of Motion in Uniform B Field?
36 Group Problem: Cyclotron Motion
A charged particle with charge q is moving with speed v in a uniform magnetic field B as shown in the figure. (1) Draw a sketch of the orbit Find (2) R : radius of the circle (3) T : period of the motion (4) : cyclotron angular
frequency 37